Knowing ref numbers of roads is good: they help for orientation, and provide a first hint on classification.
https://wiki.openstreetmap.org/wiki/Key:highway lists the road types “from most important (motorway) to least important (service)”. I.e. their importance is the major criterion for classification.
In case of ลพ.4064, the road is more likely an “unclassified”.
In contrast, the Chiang Rai bypass was built for large traffic and high speeds at a “trunk” standard. Since (currently) it ends in nowhere in the east, “trunk” is not applicable. But I think “secondary” could be a better fit than “tertiary”. And a re-tagging when the bypass gets extended.
Also ชร.5023: how important is that road? And how important is road #1 there still?
I do not know that area, that information must be supplied by people with knowledge of that place.